CN113343328A - Efficient closest point projection method based on improved Newton iteration - Google Patents

Efficient closest point projection method based on improved Newton iteration Download PDF

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CN113343328A
CN113343328A CN202110634535.4A CN202110634535A CN113343328A CN 113343328 A CN113343328 A CN 113343328A CN 202110634535 A CN202110634535 A CN 202110634535A CN 113343328 A CN113343328 A CN 113343328A
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point
curved surface
value
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closest
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CN113343328B (en
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谢冬香
齐龙
陈坚强
庞宇飞
刘杨
卢风顺
陈波
胡月凡
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The invention particularly relates to an efficient closest point projection method based on improved Newton iteration. Comprises the following steps of 1: applying an overrun interpolation method to the original CAD digital-analog curved surface to obtain three-dimensional space points, and connecting to obtain a three-dimensional grid; step 2: dispersing the original CAD digital-analog curved surface, normalizing the parameters of the original CAD digital-analog curved surface, and establishing a search tree; and step 3: searching a discrete point closest to the point to be projected by using the search tree, and obtaining a cutting ball by taking the distance between the point to be projected and the closest discrete point as a radius to obtain a screening surface and the discrete point searched on the corresponding surface; and 4, step 4: and taking the closest point of each surface after screening as an initial iteration value, and taking the closest distance point as a final projection point after circularly alternating iteration. And 5: and replacing the three-dimensional space points with the obtained projection points to obtain a grid tightly attached to the surface of the digital-analog. The method has the advantages of good grid quality, higher calculation efficiency of a real geometric model, better robustness and capability of processing discontinuous curved surfaces, and can more accurately approximate the surface of a digital-analog model.

Description

Efficient closest point projection method based on improved Newton iteration
Technical Field
The invention belongs to the technical field of simulation grid generation, and particularly relates to an efficient closest point projection method based on improved Newton iteration.
Background
In the early stages of CFD computation, a drawn mesh is required. When the surface grid is drawn, the initial grid obtained by performing the overrun interpolation on the closed boundary line is not close to the CAD model, so that the subsequent CFD calculation is inaccurate, and the grid surface can be regarded as being formed by connecting a series of ordered points, so that the problem is converted into the closest point from the solved point to the CAD model. The calculation of the closest point to any curve/surface and its corresponding parameters have numerous applications in CAD and related projects. The process of finding the optimal solution is numerical iteration based on the principle of finding the closest point, and different algorithms and numerous documents emerge in recent years aiming at the problems. Ma et al, by subdividing the NURBS surface into a number of small patches and then finding the projection results to each patch. The projection problem is processed by the aid of a recursion method by the aid of the Serimovic, and an improved algorithm for performing point projection on NURBS curves and curved surfaces is provided. Xu et al propose texture feature-based tessellation algorithms. Zhujianning and the like search for a vertex closest to a spatial point in a subdivision surface patch by using a multi-resolution sampling technology. Moon et al propose a point projection method that improves the accuracy of multistage B-spline approximation. The core idea of the above methods is based on a curve/surface subdivision algorithm.
Li et al propose a point to calculate the minimum distance on a parametric surface. Simplex et al propose a bezier curve point projection algorithm incorporating quadratic surface approximation. Xuhaiyin et al propose orthogonal projection calculations from points to implicit surfaces. Chen et al presents a problem of calculating the minimum distance between a point and a curved surface. Most of them are based on studies performed on a parametric surface. Few people also propose a method for performing nearest point projection on a model, for example, Oh and the like propose a point projection method on a free curve and a curved surface based on an efficient elimination technology. Majid et al also propose an orthogonal projection method based on heuristic random search.
Disclosure of Invention
Aiming at the existing problems, the invention provides an efficient closest point projection method based on improved Newton iteration, which does not need to subdivide a curve/curved surface, utilizes an initial value rapid positioning technology, screens the curve/curved surface by cutting circles/spheres, searches based on an improved one-way Newton iteration algorithm, finally calculates corresponding points to obtain projection points, and then replaces discrete points of a three-dimensional grid obtained by an overrun interpolation method with the projection points to finally obtain a grid attached to the surface of a digital model.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an efficient closest point projection method based on improved Newton iteration comprises the following steps:
step 1: extracting and combining boundary lines of an original CAD digital-analog curved surface, or constructing a curve on the digital-analog surface to obtain closed grid lines, taking discrete points from the grid lines in sequence and at intervals, then applying an overrun interpolation method to the closed grid lines with the discrete points to obtain three-dimensional space points in a closed grid line area, and orderly connecting the three-dimensional space points to obtain a three-dimensional grid; the points are obtained by interpolation, are not close to a CAD digital-analog curved surface, and take three-dimensional space points as points to be projected;
step 2: preprocessing an original CAD digital-analog curved surface, performing normalization processing on the original CAD digital-analog curved surface, obtaining discrete points after the parameters of the original CAD digital-analog curved surface are dispersed, and establishing a search tree;
and step 3: searching for the discrete point closest to the point to be projected of the three-dimensional grid on the original CAD digital-analog curved surface after normalization processing by using the search tree in the step 2, obtaining a cutting ball by taking the distance between the point to be projected and the closest discrete point as a radius, and excluding the curved surface where the discrete point is searched by using the cutting ball to obtain the discrete point searched on the screening surface and the corresponding surface;
and 4, step 4: taking the closest point of each surface screened in the step 3 as an initial iteration value, wherein the curved surface is a vector function of two parameters u and v, the curved surface can be represented as the mapping from a two-dimensional area on a plane to a three-dimensional space, and u and v represent the two-dimensional parameter change directions of the curved surface, so that the curved surface is regarded as being formed by infinite u-direction and v-direction parameter curves, iteration is carried out in each direction by adopting a circular alternate iteration mode of firstly carrying out the u-direction and then carrying out the v-direction, and the closest distance point is taken as a final projection point;
and 5: and (4) replacing the three-dimensional space points in the step (1) with the projection points obtained in the step (4) to finally obtain a grid attached to the surface of the digital-analog.
Preferably, the specific operation steps of step 2 include:
step 21: acquiring all bounded curved surfaces, and calculating the maximum and minimum geometric dimensions of the curved surfaces:
Figure 807558DEST_PATH_IMAGE001
，
wherein:
n +1 is the number of curved surfaces;
Figure 899755DEST_PATH_IMAGE002
is the approximate length of each facet in the u-direction;
Figure 414044DEST_PATH_IMAGE003
is the approximate length of each facet in the v-direction;
step 22: calculating the dispersion Nu and Nv of the u direction and the v direction of each curved surface:
Figure 933493DEST_PATH_IMAGE004
；
step 23: and (5) carrying out boundary value control on the discrete degree value in the step (22):
Figure 166023DEST_PATH_IMAGE005
；
wherein: minV is the minimum dispersion value and maxV is the maximum dispersion value;
step 24: solving the maximum discrete side length of each curved surface:
Figure 812643DEST_PATH_IMAGE006
；
step 25: dispersing each curved surface according to the discrete side length in the step 24 to obtain the point of the dispersed triangle and the surface information to which the point belongs, and storing the point information and the surface information in sequence;
step 26: calculating the bounding box of each surface by using the coordinate values of the discrete points in the step 25, then obtaining the periodic information of the surface through the u and v parameter values of the curved surface, and storing the periodic information as the attribute of the surface;
step 27: and establishing the AABB search tree according to the discrete points.
Preferably, the specific operation steps of step 4 are as follows:
step 41: obtaining the closest point on the curved surface S (u, v) according to the step 2
Figure 936367DEST_PATH_IMAGE007
Taking the value of v constant
Figure 895227DEST_PATH_IMAGE008
To obtain an approximate curve
Figure 346543DEST_PATH_IMAGE009
The curved surface can be approximated as a free curve in the u direction, and a vector between the curved surface and an arbitrary point P in space is expressed as a function R (u, v) in a parametric form0)：
Figure 783472DEST_PATH_IMAGE010
；
Step 42: calculating an approximation curve
Figure 535003DEST_PATH_IMAGE009
And any point in space
Figure 664764DEST_PATH_IMAGE011
Assuming the objective function is F (u, v)0) The following formula is obtained:
Figure 603376DEST_PATH_IMAGE012
，
wherein:
Figure 594728DEST_PATH_IMAGE013
is that
Figure 404028DEST_PATH_IMAGE009
Partial differential of (a);
step 43: and (5) sequentially and alternately searching the u direction and the v direction of the curved surface by adopting a Newton iteration method to obtain the closest point of the curved surface.
Preferably, the specific operation steps of step 43 include:
step 431: setting the number of circulation steps;
step 432: searching the u direction of the curved surface by adopting a one-way Newton iterative algorithm with correction, calculating the square of the distance between the discrete point searched in the step 3 and any point P, and taking the closest point S (u) as0,v0) As an initial estimate, a newton's iterative formula is obtained as follows:
Figure 439111DEST_PATH_IMAGE014
；
wherein:
Figure 583129DEST_PATH_IMAGE015
is an iteratively varied value;
Figure 361861DEST_PATH_IMAGE016
is the second derivative;
step 433: calculating a v-direction error, and terminating the search when the error reaches a threshold value;
step 434: adopting a one-way Newton iteration algorithm with correction to search the v direction of the curved surface, wherein the method is the same as the step 432;
step 435: calculating a u-direction error, and terminating the search when the error reaches a threshold value;
step 436: and storing the result of each iteration, and taking the closest point as the final projection point.
Preferably, the specific steps of step 432 include:
step 43201: inputting initial u-direction iteration step size varyU, periodicity isuPeriod and parameter value u0、v0；
Step 43202: setting the number of circulation steps;
step 43203: calculating the point S (u) on the surface0,v0) Distance to the proxel;
step 43204: judging the distance and the error value, and ending the circulation when the distance is smaller than the error value;
step 43205: calculating the first derivative Su(u,v0)；
Step 43206: calculating the second directional derivative Suu(u,v0)；
Step 43207: calculating the point S (u) on the surface0,v0) Directions R (u, v) to the projection point0)；
Step 43208: when R (u, v)0) * Su(u,v0) When the error value is smaller than the error value, calculating an adjustment parameter;
step 43209: calculating an angle value;
step 43210: if the angle value is less than the error value, ending the loop;
step 43211: calculating the change of the u-direction parameters;
step 43212: if the angle value is less than the error value, ending the loop;
step 43213: initializing a direction variable isReverse = false, and an initial correction value ratio = 1.0;
step 43214: performing parameter correction algorithm circularly, and correcting the direction R (u, v) of the projection point0) Greater than the projection point direction R (u, v) before correction0) And ending the loop when the direction variable isReverse = true;
step 43215: calculating the change of the u-direction parameters;
step 43216: if the angle value is less than the error value, ending the loop;
step 43217: updating parameter value u0。
Preferably, the specific steps of the parameter correction algorithm of step 43208 include:
step 432081: an initial correction value ratio and an initialization direction variable isReverse;
step 432082: if the initial correction value ratio is less than the threshold value t0When the ratio is greater than 0, setting the ratio to be-1 and marking the direction isReverse to be true;
step 432083: if the initial correction value ratio is greater than the threshold value t0And when ratio is less than 0, update the value, correct the boundary and end the loop.
Compared with the prior art, the invention has the beneficial effects that:
compared with the classic Newton bilateral iteration, the effect of the one-way Newton iteration is more ideal in solving the nearest point, the projection of the classic Newton bilateral iteration is trapped in the local minimum value at the crease, the iterative algorithm of the invention well solves the problem, the projected grid of the invention has good overall quality, and can approach the surface of a digital model more accurately. Moreover, the method provided by the invention has higher calculation efficiency on the real geometric model, better robustness, capability of well processing the problems of discontinuous curved surface and the like, and can meet the engineering requirements.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
In the drawings:
FIG. 1 is a schematic flow chart of an efficient closest point projection method based on improved Newton iteration according to the present invention;
FIG. 2 is a surface diagram of the efficient closest point projection method based on improved Newton iteration;
FIGS. 3(a) - (c) are respectively a mesh surface generation front surface graph, a classic Newton bilateral iteration method projection effect graph and an improved Newton iteration based efficient closest point projection method projection effect graph of the efficient closest point projection method based on the improved Newton iteration;
FIGS. 4(a) - (b) are respectively a Layer model before-projection effect graph and a Layer model after-projection effect graph of the efficient closest point projection method based on improved Newton iteration;
FIGS. 5(a) - (b) are respectively a pre-projection effect diagram and a post-projection effect diagram of the f6 standard model pod based on the efficient closest point projection method for improving Newton iteration;
FIGS. 6(a) - (b) are respectively a submarine model tail projection front effect diagram and a submarine model tail projection rear effect diagram based on the high-efficiency closest point projection method for improving Newton iteration;
FIGS. 7(a) - (b) are a pre-projection effect diagram and a post-projection effect diagram of an aircraft model based on the efficient closest point projection method for improving Newton iteration according to the present invention, respectively;
FIGS. 8(a) - (b) are a pre-projection effect diagram and a post-projection effect diagram of the head of the Hb-2 model based on the efficient closest point projection method for improving Newton iteration;
FIGS. 9(a) - (b) are respectively a pre-projection effect graph and a post-projection effect graph of the external surface of the screen model based on the efficient closest point projection method for improving Newton iteration;
FIG. 10 is a boundary line of an original CAD digital-to-analog curved surface of the model denoted by F6;
FIG. 11 is a closed boundary line with discrete points of an original CAD digital-analog curved surface of the model denoted by F6;
FIG. 12 is a grid obtained by applying an overrun interpolation method to an original CAD digital-to-analog curved surface of the F6 model;
FIG. 13 shows a mesh obtained by applying the method of the present invention to an original CAD digital-to-analog curved surface of a model denoted by F6.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
With reference to fig. 1-13, an efficient closest point projection method based on modified newton iteration can be implemented to generate a grid, including the following steps:
step 1: extracting and combining boundary lines of an original CAD digital-analog curved surface, or constructing a curve on the digital-analog surface to obtain closed grid lines, taking discrete points from the grid lines in sequence and at intervals, then applying an overrun interpolation method to the closed grid lines with the discrete points to obtain three-dimensional space points in a closed grid line area, and orderly connecting the three-dimensional space points to obtain a three-dimensional grid; the points are obtained by interpolation, are not close to the CAD digital-analog curved surface, and take three-dimensional space points as points to be projected.
Step 2: and (3) preprocessing the original CAD digital-analog curved surface, performing normalization processing on the original CAD digital-analog curved surface, obtaining discrete points after the parameters are dispersed, and establishing a search tree. The method comprises the following specific steps:
step 21: acquiring all bounded curved surfaces and calculating the maximum and minimum geometric dimensions of the curved surfaces:
Figure 291246DEST_PATH_IMAGE001
，
wherein:
n +1 is the number of curved surfaces;
Figure 231651DEST_PATH_IMAGE002
is the approximate length of each facet in the u-direction;
Figure 879277DEST_PATH_IMAGE003
is the approximate length of each facet in the v-direction.
Step 22: calculating the discrete degree Nu and Nv of each surface u and v direction:
Figure 196120DEST_PATH_IMAGE004
。
step 23: and (5) carrying out boundary value control on the discrete degree value in the step (22):
Figure 269028DEST_PATH_IMAGE005
，
wherein: minV is the minimum discrete value, and min is taken as 3; maxV is the maximum dispersion value, taking max to be 100.
Step 24: calculating the maximum discrete side length:
Figure 380335DEST_PATH_IMAGE006
。
step 25: and (4) dispersing each curved surface according to the discrete side length in the step (24) to obtain the point of the dispersed triangle and the surface information to which the point belongs, and storing the point information and the surface information in sequence.
Step 26: and calculating the bounding box of each surface by using the coordinate values of the discrete points in the step 25, then obtaining the periodicity information of the surface through the u and v parameter values of the curved surface, and storing the periodicity information as the attribute of the surface.
Step 27: and establishing the AABB search tree according to the discrete points.
And step 3: searching for the discrete point closest to the point to be projected of the three-dimensional grid on the original CAD digital-analog curved surface after normalization processing by using the search tree in the step 2, obtaining a cutting ball by taking the distance between the point to be projected and the closest discrete point as a radius, and excluding the curved surface where the discrete point is searched by using the cutting ball to obtain the discrete point searched on the screening surface and the corresponding surface;
and 4, step 4: and 3, taking the closest point of each surface screened in the step 3 as an initial iteration value, wherein the curved surface is a vector function of two parameters u and v, the curved surface can be represented as the mapping from a two-dimensional area on a plane to a three-dimensional space, and u and v represent the two-dimensional parameter change directions of the curved surface, so that the curved surface is regarded as being formed by infinite u-direction and v-direction parameter curves, iteration is carried out in each direction by adopting a mode of circularly and alternately iterating the u direction and the v direction, and the closest distance point is taken as a final projection point. The method comprises the following specific steps:
step 41: obtaining the closest point on the curved surface S (u, v) according to the step 2
Figure 515257DEST_PATH_IMAGE007
Taking the value of v constant
Figure 635791DEST_PATH_IMAGE008
To obtain an approximate curve
Figure 290501DEST_PATH_IMAGE009
The curved surface can be approximated as a free curve in the u direction, and a vector between the curved surface and an arbitrary point P in space is expressed as a function R (u, v) in a parametric form0)：
Figure 838288DEST_PATH_IMAGE010
；
Step 42: calculating an approximation curve
Figure 178615DEST_PATH_IMAGE009
And any point in space
Figure 102839DEST_PATH_IMAGE011
Assuming the objective function is F (u, v)0) The following formula is obtained:
Figure 877635DEST_PATH_IMAGE012
，
wherein:
Figure 596324DEST_PATH_IMAGE013
is that
Figure 440258DEST_PATH_IMAGE009
Partial differential of (a);
step 43: the method for finding the closest point of the curved surface by sequentially and alternately searching the u direction and the v direction of the curved surface by adopting a Newton iteration method specifically comprises the following steps:
step 431: the number of cycle steps is set.
Step 432: searching the direction of the curved surface u by adopting a one-way Newton iterative algorithm with correction, calculating the square of the distance between the discrete point searched in the step 3 and any point P, and taking the closest point S (u) as0,v0) As an initial estimate, a newton's iterative formula is obtained as follows:
Figure 902595DEST_PATH_IMAGE014
，
wherein:
Figure 515585DEST_PATH_IMAGE015
is an iteratively varied value;
Figure 405175DEST_PATH_IMAGE016
is the second derivative.
The method comprises the following specific steps:
step 43201: inputting initial u-direction iteration step size varyU, periodicity isuPeriod and parameter value u0、vi；
Step 43202: setting the number of circulation steps;
step 43203: calculating the point S (u) on the surface0,v0) Distance to the proxel;
step 43204: judging the distance and the error value, and ending the circulation when the distance is smaller than the error value;
step 43205: calculating the first derivative Su(u,v0)；
Step 43206: calculating the second directional derivative Suu(u,v0)；
Step 43207: calculating the point S (u) on the surface0,v0) Directions R (u, v) to the projection point0)；
Step 43208: when R (u, v)0) * Su(u,v0) When the error value is smaller than the error value, the calculation of the adjustment parameter specifically includes:
step 432081: an initial correction value ratio and an initialization direction variable isReverse;
step 432082: if the initial correction value ratio is less than the threshold value t0When the ratio is greater than 0, setting the ratio to be-1 and marking the direction isReverse to be true;
step 432083: if the initial correction value ratio is greater than the threshold value t0When the ratio is less than 0, updating a value, correcting the boundary and ending the cycle;
step 43209: calculating an angle value;
step 43210: if the angle value is less than the error value, ending the loop;
step 43211: calculating the change of the u-direction parameters;
step 43212: if the angle value is less than the error value, ending the loop;
step 43213: initializing a direction variable isReverse = false, and an initial correction value ratio = 1.0;
step 43214: performing parameter correction algorithm circularly, and correcting the direction R (u, v) of the projection point0) Greater than the projection point direction R (u, v) before correction0) And ending the loop when the direction variable isReverse = true;
step 43215: calculating the change of the u-direction parameters;
step 43216: if the angle value is less than the error value, ending the loop;
step 43217: updating parameter value u0。
Step 433: calculating a v-direction error, and terminating the search when the error reaches a threshold value;
step 434: adopting a one-way Newton iteration algorithm with correction to search the direction of the curved surface v, wherein the method is the same as the step 432;
step 435: calculating a u-direction error, and terminating the search when the error reaches a threshold value;
step 436: and storing the result of each iteration, and taking the closest point as the final projection point.
Examples
Example demonstration and quality check
(1) Layer model
In order to verify the efficient closest point projection method based on the improved Newton iteration, a Layer model is used for projection, and the result is checked;
fig. 4(a) is a diagram of the effect of the Layer model before projection, and fig. 4(b) is a diagram of the effect of the Layer model after projection.
(2) f6 standard model nacelle
Using f6 standard model pod to project and check the result;
FIG. 5(a) is a diagram showing the effect of the model pod f6 before projection, and FIG. 5(b) is a diagram showing the effect of the model pod f6 after projection.
(3) Submarine model tail
Projecting by using the tail part of the submarine model, and checking the result;
FIG. 6(a) is an effect diagram before submarine model tail projection, and FIG. 6(b) is an effect diagram after submarine model tail projection.
(4) Model of an aircraft
Projecting by using a certain aircraft model, and checking the result;
fig. 7(a) is a projected front effect diagram of an aircraft model, and fig. 7(b) is a projected rear effect diagram of the aircraft model.
(5) Hb-2 model head
Using the head of the Hb-2 model to perform projection, and checking the result;
FIG. 8(a) is a diagram of the effect of the Hb-2 head model before projection, and FIG. 8(b) is a diagram of the effect of the Hb-2 head model after projection.
(6) Outer surface of screen model
Projecting by using the outer surface of the screen model, and checking the result;
fig. 9(a) is a diagram of an effect of the external surface of the screen model before projection, and fig. 9(b) is a diagram of an effect of the external surface of the screen model after projection.
(7) F6 Standard model outline surface
The boundary line of the original CAD digital-analog curved surface of the F6 standard model is shown in FIG. 10, four closed grid lines are obtained by extracting and combining the boundary line, and the same discrete points are taken from the four grid lines according to opposite sides, as shown in FIG. 11; then applying an overrun interpolation method to the closed grid lines with the discrete points to obtain three-dimensional space points in the closed grid line area, and orderly connecting the three-dimensional space points to obtain a three-dimensional grid, wherein the three-dimensional grid is not close to the CAD digital-analog curved surface, as shown in FIG. 12; then, preprocessing an original CAD digital-analog curved surface, carrying out normalization processing on the original CAD digital-analog curved surface, obtaining discrete points after the parameters are dispersed, and establishing a search tree; searching the discrete points closest to the point to be projected of the three-dimensional grid on the curved surface after normalization processing by using the obtained search tree, obtaining a cutting ball by taking the distance between the point to be projected and the closest discrete points as a radius, and eliminating the given curved surface by using the cutting ball to obtain the discrete points searched on the screening surface and the corresponding surface; taking the closest point of each surface after screening as an initial iteration value, regarding the curved surface as being formed by an infinite u-direction and v-direction parameter curve, performing iteration in each direction by adopting a circular alternate iteration mode of firstly performing u-direction iteration and then performing v-direction iteration, and taking the closest distance point as a final projection point; and (3) replacing the obtained projection points with three-dimensional space points to finally obtain a grid close to the surface of the digital-analog, as shown in fig. 13.
As can be seen from the drawings, for the actual engineering digital analogy, the grid projected by the method provided by the invention has good overall quality, can approach the surface of the digital analogy more accurately, can well solve the problems of discontinuous curved surface and the like, and meets the engineering requirements.
Conclusion of the experiment
According to the verification process, the high-efficiency closest point projection method based on the improved Newton iteration has good overall quality of the projected grid, and can approach the surface of a digital-analog more accurately. The method has higher calculation efficiency on the real geometric model, better robustness and can well process the problems of surface discontinuity and the like.
In addition, the method can also be used for generating the grid lines of the skin, and the principle is the same as the grid surface of the net.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (6)

1. An efficient closest point projection method based on improved Newton iteration is characterized in that: the method comprises the following steps:
step 1: extracting and combining boundary lines of an original CAD digital-analog curved surface, or constructing a curve on the digital-analog surface to obtain closed grid lines, taking discrete points from the grid lines in sequence and at intervals, then applying an overrun interpolation method to the closed grid lines with the discrete points to obtain three-dimensional space points in a closed grid line area, and orderly connecting the three-dimensional space points to obtain a three-dimensional grid; the points are obtained by interpolation, are not close to a CAD digital-analog curved surface, and take three-dimensional space points as points to be projected;
step 2: preprocessing an original CAD digital-analog curved surface, performing normalization processing on the original CAD digital-analog curved surface, obtaining discrete points after the parameters of the original CAD digital-analog curved surface are dispersed, and establishing a search tree;
and step 3: searching for the discrete point closest to the point to be projected of the three-dimensional grid on the original CAD digital-analog curved surface after normalization processing by using the search tree in the step 2, obtaining a cutting ball by taking the distance between the point to be projected and the closest discrete point as a radius, and excluding the curved surface where the discrete point is searched by using the cutting ball to obtain the discrete point searched on the screening surface and the corresponding surface;
and 4, step 4: taking the closest point of each surface screened in the step 3 as an initial iteration value, wherein the curved surface is a vector function of two parameters u and v, the curved surface can be represented as the mapping from a two-dimensional area on a plane to a three-dimensional space, and u and v represent the two-dimensional parameter change directions of the curved surface, so that the curved surface is regarded as being formed by infinite u-direction and v-direction parameter curves, iteration is carried out in each direction by adopting a circular alternate iteration mode of firstly carrying out the u-direction and then carrying out the v-direction, and the closest distance point is taken as a final projection point;
and 5: and (4) replacing the three-dimensional space points in the step (1) with the projection points obtained in the step (4) to finally obtain a grid attached to the surface of the digital-analog.
2. The efficient closest point projection method based on improved Newton iteration as claimed in claim 1, wherein: the specific operation steps of the step 2 comprise:
step 21: acquiring all bounded curved surfaces, and calculating the maximum and minimum geometric dimensions of the curved surfaces:
Figure 203701DEST_PATH_IMAGE001
，
wherein:
n +1 is the number of curved surfaces;
Figure 137153DEST_PATH_IMAGE002
is the approximate length of each facet in the u-direction;
Figure 664693DEST_PATH_IMAGE003
is the approximate length of each facet in the v-direction;
step 22: calculating the dispersion Nu and Nv of the u direction and the v direction of each curved surface:
Figure 810635DEST_PATH_IMAGE004
；
step 23: and (5) carrying out boundary value control on the discrete degree value in the step (22):
Figure 396247DEST_PATH_IMAGE005
；
wherein: minV is the minimum dispersion value and maxV is the maximum dispersion value;
step 24: solving the maximum discrete side length of each curved surface:
Figure 969442DEST_PATH_IMAGE006
；
step 25: dispersing each curved surface according to the discrete side length in the step 24 to obtain the point of the dispersed triangle and the surface information to which the point belongs, and storing the point information and the surface information in sequence;
step 26: calculating the bounding box of each surface by using the coordinate values of the discrete points in the step 25, then obtaining the periodic information of the surface through the u and v parameter values of the curved surface, and storing the periodic information as the attribute of the surface;
step 27: and establishing the AABB search tree according to the discrete points.
3. The efficient closest point projection method based on improved Newton iteration as claimed in claim 2, wherein: the specific operation steps of the step 4 are as follows:
step 41: obtaining the closest point on the curved surface S (u, v) according to the step 2
Figure 984278DEST_PATH_IMAGE007
Taking the value of v constant
Figure 933911DEST_PATH_IMAGE008
To obtain an approximate curve
Figure 350592DEST_PATH_IMAGE009
The curved surface can be approximated as a free curve in the u direction, and a vector between the curved surface and an arbitrary point P in space is expressed as a function R (u, v) in a parametric form0)：
Figure 360268DEST_PATH_IMAGE010
；
Step 42: calculating an approximation curve
Figure 862400DEST_PATH_IMAGE009
And any point in space
Figure 350144DEST_PATH_IMAGE011
Assuming the objective function is F (u, v)0) The following formula is obtained:
Figure 886911DEST_PATH_IMAGE012
，
wherein:
Figure 67488DEST_PATH_IMAGE013
is that
Figure 322496DEST_PATH_IMAGE009
Partial differential of (a);
step 43: and (5) sequentially and alternately searching the u direction and the v direction of the curved surface by adopting a Newton iteration method to obtain the closest point of the curved surface.
4. The efficient closest point projection method based on improved Newton iteration as claimed in claim 3, wherein: the specific operation of step 43 includes:
step 431: setting the number of circulation steps;
step 432: searching the u direction of the curved surface by adopting a one-way Newton iterative algorithm with correction, calculating the square of the distance between the discrete point searched in the step 3 and any point P, and taking the closest point S (u) as0,v0) As an initial estimate, a newton's iterative formula is obtained as follows:
Figure 348351DEST_PATH_IMAGE014
；
wherein:
Figure 739625DEST_PATH_IMAGE015
is an iteratively varied value;
Figure 838906DEST_PATH_IMAGE016
is the second derivative;
step 433: calculating a v-direction error, and terminating the search when the error reaches a threshold value;
step 434: adopting a one-way Newton iteration algorithm with correction to search the v direction of the curved surface, wherein the method is the same as the step 432;
step 435: calculating a u-direction error, and terminating the search when the error reaches a threshold value;
step 436: and storing the result of each iteration, and taking the closest point as the final projection point.
5. The efficient closest point projection method based on improved Newton iteration as claimed in claim 4, wherein: the specific steps of step 432 include:
step 43201: input deviceInitial u-direction iteration step size varyU, periodic isuPeriod and parameter value u0、v0；
Step 43202: setting the number of circulation steps;
step 43203: calculating the point S (u) on the surface0,v0) Distance to the proxel;
step 43204: judging the distance and the error value, and ending the circulation when the distance is smaller than the error value;
step 43205: calculating the first derivative Su(u,v0)；
Step 43206: calculating the second directional derivative Suu(u,v0)；
Step 43207: calculating the point S (u) on the surface0,v0) Directions R (u, v) to the projection point0)；
Step 43208: when R (u, v)0) * Su(u,v0) When the error value is smaller than the error value, calculating an adjustment parameter;
step 43209: calculating an angle value;
step 43210: if the angle value is less than the error value, ending the loop;
step 43211: calculating the change of the u-direction parameters;
step 43212: if the angle value is less than the error value, ending the loop;
step 43213: initializing a direction variable isReverse = false, and an initial correction value ratio = 1.0;
step 43214: performing parameter correction algorithm circularly, and correcting the direction R (u, v) of the projection point0) Greater than the projection point direction R (u, v) before correction0) And ending the loop when the direction variable isReverse = true;
step 43215: calculating the change of the u-direction parameters;
step 43216: if the angle value is less than the error value, ending the loop;
step 43217: updating parameter value u0。
6. The efficient closest point projection method based on modified Newton's iteration as claimed in claim 5, wherein: the specific steps of the parameter correction algorithm of step 43208 include:
step 432081: an initial correction value ratio and an initialization direction variable isReverse;
step 432082: if the initial correction value ratio is less than the threshold value t0When the ratio is greater than 0, setting the ratio to be-1 and marking the direction isReverse to be true;
step 432083: if the initial correction value ratio is greater than the threshold value t0And when ratio is less than 0, update the value, correct the boundary and end the loop.
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